Can a photon have energy of spin?

I have been asking myself of late whether or not the energy of a fundamental (point-like) particle has a component attributable to its spin. My understanding has been that a point-like particle has no energy of spin because its moment of inertia is zero.

This article appears to both agree and to imply the opposite (see words in bold below):

Competition between spin and orbital photon angular momentum transfer in liquid crystals
Abstract:
We present a theoretical and experimental study on the transfer of angular momentum from a light beam to a nematic liquid crystal film. In the angular momentum transfer process photons are not destroyed, but scattered in a different angular momentum state: a process known as self-induced stimulated light scattering (Santamato E, Daino B, Romagnoli M, Settembre M and Shen Y R 1988 Phys. Rev. Lett. 61 113-16). Each photon in the incident beam transfers to the material only the change of its angular momentum, producing a torque on the body. Under the action of this torque, the body starts to rotate, changing, in turn, the amount of angular momentum extracted from the light beam. The process is intrinsically nonlinear and, as proved by the experiments reported in this paper, it can be initiated by a light beam carrying no angular momentum at all.

And yet this implies we can compute an amount of rotational energy contributed by each photon, i.e. the rotational kinectic energy of the body divided by the number of photons "scattered" by the body.

A way out of this paradox may be in the words "spin" and "orbital", which appear in the title but not the abstract. I have not read the article itself, as I am uncertain the access fee will purchase enlightenment or just regret about the $24.

Any "energy associated with spin" has nothing to do with the article you cited. The point there is that angular momentum is a vector quantity, so whilst you can't have negative energies, you can have a system with zero total angular momentum whose components start spinning so long as their separate angular momenta add up to zero.

As for your original question, I think you're right that it makes no contribution to the energy. The idea of a particle as an infinitesmal ball spinning about some axis is misleading anyway; spin is a fundamental property of elementary particles, like charge. (Quantum mechanically it's associated with a degeneracy of states that transform into each other under rotations; spin only affects the energy when something like a magnetic field spoils this degeneracy by picking out a preferred direction). Any energy associated with spin would be present in the particle at rest, so there'd be no way of separating it out from the rest energy E=mc^2 of the particle anyway.

Thank you for your thoughtful reply. Your final observation was particularly convincing.

Nevertheless, it seems to me that the abstract cannot be right in saying "Each photon in the incident beam transfers to the material only the change of its angular momentum". The material is acquiring rotational kinetic energy from the light beam as well as angular momentum which is equal and opposite to the angular momentum (spin or orbital?) of the "scattered" photons. I use quotes here because the abstract applies "scattered" to angular momentum states and not to the relatively familiar concept (for me) of linear momentum states. But no change of linear momentum implies no transfer of energy to the material. So where does the material get its rotational energy? Perhaps they explain it all in their paper.

And thank you. Your comments give me a feel for the correct form of the answer to my question, except for the aforementioned details raised in the paper. Therefore, the particle addressing you remains grateful, but in a slightly disturbed state of confusion.